(1) Field of the Invention
The present invention relates to a method for measuring mechanical characteristics of materials. More particularly, this invention provides a method which uses transfer functions obtained by insonifying the material at different angles. Once obtained, the transfer functions are manipulated to yield closed form values of dilatational and shear wavespeeds. The wavespeeds are combined to determine complex Lamé constants, complex Young's modulus, complex shear modulus, and complex Poisson's ratio for the material.
(2) Description of the Prior Art
Measuring the mechanical properties of slab-shaped (i.e., plates) materials are important in that these parameters significantly contribute to the static and dynamic response of structures built with such materials. Resonant techniques have been used to identify and measure longitudinal properties for many years (See D. M. Norris, Jr., and W. C. Young, “Complex Modulus Measurements by Longitudinal Vibration Testing,” Experimental Mechanics, Volume 10, 1970, pp. 93–96; W. M. Madigosky and G. F. Lee, “Improved Resonance Technique for Materials Characterization,” Journal of the Acoustical Society of America, Volume 73, Number 4, 1983, pp. 1374–1377; S. L. Garrett, “Resonant Acoustic Determination of Elastic Moduli,” Journal of the Acoustical Society of America, Volume 88, Number 1, 1990, pp. 210–220; G. F. Lee and B. Hartmann, U.S. Pat. No. 5,363,701; G. W. Rhodes, A. Migliori, and R. D. Dixon, U.S. Pat. No. 5,495,763; and R. F. Gibson and E. O. Ayorinde, U.S. Pat. No. 5,533,399).
These methods are based on comparing the measured eigenvalues of a structure to predicted eigenvalues from a model of the same structure. The model of the structure must have well-defined (typically closed form) eigenvalues for these methods to work. Additionally, resonant techniques only allow measurements at resonant frequencies. Most of these methods typically do not measure shear wavespeeds (or modulus) and do not have the ability to estimate Poisson's ratio.
Comparison of analytical models to measured frequency response functions is another method used to estimate stiffness and loss parameters of a structure (See B. J. Dobson, “A Straight-Line Technique for Extracting Modal Properties From Frequency Response Data,” Mechanical Systems and Signal Processing, Volume 1, 1987, pp. 29–40; T. Pritz, “Transfer Function Method for Investigating the Complex Modulus of Acoustic Materials: Rod-Like Specimen,” Journal of Sound and Vibration, Volume 81, 1982, pp. 359–376; W. M. Madigosky and G. F. Lee, U.S. Pat. No. 4,352,292; and W. M. Madigosky and G. F. Lee, U.S. Pat. No. 4,418,573). When the analytical model agrees with one or more frequency response functions, the parameters used to calculate the analytical model are considered accurate. If the analytical model is formulated using a numerical method, a comparison of the model to the data can be difficult due to dispersion properties of the materials.
Another method to measure stiffness and loss is to deform the material and measure the resistance to the indentation (See W. M. Madigosky, U.S. Pat. No. 5,365,457). However, this method can physically damage the specimen if the deformation causes the sample to enter the plastic region of deformation.
Others methods have used insonification as a means to determine defects in composite laminate materials (See D. E. Chimenti and Y. Bar-Cohen, U.S. Pat. No. 4,674,334). However, these methods do not measure material properties.
A method does exist to measure shear wave velocity and Poisson's ratio in the earth using boreholes and seismic receivers (See J. D. Ingram and O. Y. Liu, U.S. Pat. No. 4,633,449). However, this method needs a large volume of material and is not applicable to slab-shaped samples. Additionally, it needs a borehole in the volume at some location.
In view of the above, there is a need for a method to measure complex frequency-dependent dilatational and shear wavespeeds of materials subject to insonification. Once the wavespeeds are identified, the complex frequency-dependent Young's and shear moduli and complex frequency-dependent Poisson's ratio can also be measured (or estimated).